For the following cases, you may use either the P-value approach or the rejection region approach to present a full hypothesis test, including:Identifying the claim and H0 and Ha,Finding the appropriate standardized test statistic,Finding the P-value or the rejection region,Deciding whether to reject or fail to reject the null hypothesis, andInterpreting the decision in the context of the original claim. A guidance counselor claims that high school students in a college preparatory program score higher on the ACT test than those in a general program. The mean ACT score for a random sample of 49 students in the college preparatory program is 22.2 with a standard deviation of 4.8. The mean ACT score for a random sample of 46 students in the general program is 20.0 with a standard deviation of 5.4. Perform the appropriate test on the counselor’s claim with regard to the difference between the mean ACT scores at α = 0.10.

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Description: For the following cases, you may use either the P-value approach or the rejection region approach to present a full hypothesis test, including:Identifying the claim and H0 and Ha,Finding the appropriate standardized test statistic,Finding the P-value

GivenCollege preparatory programGeneral program 1)There are two samples and population standard…

Answered: For the following cases, you may use…

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter12: Probability

Section12.CR: Chapter 12 Review

Problem 16CR

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For the following cases, you may use either the P-value approach or the rejection region approach to present a full hypothesis test, including:

Identifying the claim and H₀and H_a,
Finding the appropriate standardized test statistic,
Finding the P-value or the rejection region,
Deciding whether to reject or fail to reject the null hypothesis, and
Interpreting the decision in the context of the original claim.

A guidance counselor claims that high school students in a college preparatory program score higher on the ACT test than those in a general program. The mean ACT score for a random sample of 49 students in the college preparatory program is 22.2 with a standard deviation of 4.8. The mean ACT score for a random sample of 46 students in the general program is 20.0 with a standard deviation of 5.4. Perform the appropriate test on the counselor’s claim with regard to the difference between the mean ACT scores at α = 0.10.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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